Its only a test of the concept, but It turns out great

How do you relate number, proportion and sound within sacred geometry, and where do you draw the line between a proportion with a mathematical basis and a symbolic numerology?

I’m a musician, and for several years now I’ve been down a rabbit hole that started with the book Healing Codes for the Biological Apocalypse (1999) by Leonard Horowitz and Joseph Puleo. It’s the book behind the so-called Solfeggio frequencies, a six-tone scale that, according to the authors, was used in ancient chants and was “hidden” by the ecclesiastical authorities

What is documented is medieval. The syllables we use to sing the scale (do, re, mi, fa, sol, la, si) come from a Latin hymn to Saint John the Baptist, Ut queant laxis, attributed to Paul the Deacon (8th century). In the 11th century, the Benedictine monk Guido d’Arezzo used it to teach singers the pitch of the notes: the melody rose one note with each line, so remembering the first syllable of each line was enough

Ut queant laxis

Resonare fibris,

Mira gestorum

Famuli tuorum,

Solve polluti

Labii reatum,

Sancte Ioannes

A free translation: “So that your servants may, with loosened voices, resound the wonders of your deeds, cleanse the guilt from their stained lips, Saint John”

Here is how each note lines up with the hymn:

C: Do (formerly Ut), from “Ut queant laxis”

D: Re, from “Resonare fibris”

E: Mi, from “Mira gestorum”

F: Fa, from “Famuli tuorum”

G: Sol, from “Solve polluti”

A: La, from “Labii reatum”

B: Si, from “Sancte Ioannes”

Guido worked with six notes. The seventh, Si, was added centuries later, built from the initials of Sancte Ioannes, between the late 16th and early 17th centuries. In that same century, the Italian theorist Giovanni Battista Doni changed Ut to Do because it was easier to sing. Also, those syllables indicated relative pitches within a hexachord, not fixed frequencies

According to Horowitz and Puleo, each of the six syllables corresponds to a frequency they rediscovered through a numerological analysis of the Book of Numbers in the Bible (chapter 7, verses 12 to 83). Their method reduces numbers to a single digit (digital root), and they claim a repeating pattern of 3, 6 and 9 appears, the same numbers from the phrase attributed to Nikola Tesla about “the key to the universe”:

Do: 396 Hz (3+9+6 = 18 → 9). Liberating guilt and fear; turning grief into joy.

Re: 417 Hz (4+1+7 = 12 → 3). Facilitating change; undoing trauma and crystallized patterns.

Mi: 528 Hz (5+2+8 = 15 → 6). The “miracle note”; transformation and DNA repair.

Fa: 639 Hz (6+3+9 = 18 → 9). Connection, relationships and harmony.

Sol: 741 Hz (7+4+1 = 12 → 3). Intuition, self-expression and cellular cleansing.

La: 852 Hz (8+5+2 = 15 → 6). Spiritual order; seeing through illusions.

Horowitz later expanded the scale to nine tones, adding 174 Hz (security and easing pain), 285 Hz (tissue regeneration) and 963 Hz (return to unity)

The relationship between number and sound does have an ancient and solid basis: the Pythagorean tradition expressed musical intervals as ratios of whole numbers (the octave 2:1, the fifth 3:2, the fourth 4:3). That is proportion with a physical foundation, and it is very different from reducing biblical numbers to a single digit. I’m very interested in the difference between the two: a proportion that can be measured, constructed and verified, and a symbolic correspondence that works by convention

Of all the frequencies, the one I’m most drawn to is 396 Hz, associated in this system with release from fear and with grounding. That made me think of plants, which literally live by being rooted, and I built an installation: a group of plants connected to a Playtronica circuit. This circuit transforms the plants’ bioelectric signals: when someone touches a plant, it detects the change in conductivity and sends a MIDI note-on that triggers a synth tuned to 396 Hz. No touch, no sound. When you touch it, the plant “answers” with that tone

I bring it here as an example of sound, number and living form brought together in an object you can touch

Where do you draw the line between a proportion with a mathematical basis (harmonic ratios, the golden ratio, constructible polygons) and a symbolic numerology like the digital root? How do you work with sound and geometry together? Do you know of examples of resonance figures (such as Chladni patterns or cymatics) that help show the relationship between frequency and form? Do you think it’s legitimate to use symbolic systems that aren’t historically true as a tool for contemplation, or do you prefer to stick with what’s verifiable?

If anyone is interested in seeing how the circuit is wired and hearing how it sounds, I recorded a video of the setup and the plants responding. I’m happy to share it here with anyone who’s interested. I can also walk through the build (MIDI mapping, synth tuning, touch detection). No pressure at all, I’m here mostly for the conversation and to learn from those who know more about geometry. Thanks for reading 🌱

Very niceeee… sorry for movement, I’ll start propping up my phone for this

@Sols222creations on Instagram

"A Peace From My Soul" Acrylic on 48’x48’ in. canvas. I’ll have my own art exhibit one day. I know it.

You guys might remember my stacking designs. Well, I have a lot in store for you all!

There’s a lot to this, and you can check out my other posts for my write up, but essentially I discovered a new class of shapes.

The other posts aren’t performing so well, so I am posting this as a video because it really helps show off the work.

Stay tuned for more to come! Thanks!

A few weeks back, after many iterations of the fractal torus model, I created an algorithmic artwork called Tortoise, made in tandem with AI. As part of the Nameless framework, I had landed on the Hopf fibration as an important structure for defining physical reality. I took an artistic leap after this... overlaying two oppositely rotated Hopf fibre bundles, then repeating the whole structure again and again at the interstices formed by their intersections, to form a fractal torus. This differs from other torus visualisations I've seen, not only in its use of Hopf fibres, but in the fractal arrangement, which produces that "many, many eyes" quality or the "wheels within wheels" quality.

Studying it from different angles, I realised, to my shock, that this structure had many many connections to scientific concepts, myths and symbols across the world and across history:

Science: the black hole and white hole paradigm, wormholes

Sacred geometry: Flower of Life, Lotus of Life, Triskelion, Yin Yang

Religious symbols: Sri Yantra on Kurma, Shatkona, Swastika, Tree of Life, Thousand Petalled Lotus, Reclining Vishnu, Samudra Manthan, Shivlingam, Avalokiteshvara, Ezekiel's Wheel, the Celtic Cross

Sacred architecture: Muqarnas and Islamic geometric patterns, Rose windows

Visionary art made in altered states, such as Alex Grey's

Contemporary design: even the OpenAI logo

To show how all these might derive from one source, I built a system that varies the parameters of the same root Tortoise artwork until it matches each symbol. Then I made a visualiser where you can click any symbol, read about the connection, and study the match visually.

I'm not claiming these are all derived from this single structure. Each connection is pattern-matched at this stage, and the scientific ones especially are speculative. I claim only the visual match, not an actual connection. But there are too many to ignore. Perhaps what the ancients meditated upon is the same structure science is reaching towards, and the same structure seen in altered states of consciousness. If the universe is sound based, perhaps the wave-structure formed by the primordial sound corresponds to a similar fractal torus structure?

Many of these connections already exist in literature and in esoteric theory. Some were abstract, some pointed directly to a torus, though not, as far as I know, to this particular variation. This is therefore a synthesis of many people's work over millennia, seen through the lens of my own. I'm assembling it with humility and respect, hoping we notice that we are all telling the same story through different lenses.

I have made 26 connections so far, and I hope to add more. I'm giving equal weight to each tradition, so if you spot flaws or biases in the text or visual, they aren't intentional, and I hope to improve these over time.

Artwork “Tortoise” and the visualiser at: https://nurecas.com/tortoise?o

I keep seeing new lines and patterns as I watch this. Some of those patterns echo the designs found in Metatron's cube.

To see this cover the plane go to https://cunews.info/HexPrisms.html On the page the tile is kind of big. On the Mac and on Firefox you can zoom out by hitting command -.

Hexagonal array layers are scaled by the harmonic sequence: 1, 1/2, 1/3, 1/4, 1/5, etc.